VI. The equation of state

The present paper is concerned with the study of an approximate equation of state, first derived by Green, which covers both phases, liquid and gas, and can be used for numerical evaluation. It contains explicitly the roots of a certain transcendental equation. The difference between the liquid and the gas corresponds to the existence or non-existence of real roots of this equation. The solution of the transcendental equation has been reduced, by using a suitable expansion, to the solution of an algebraic equation. In this way explicit expressions for the equation of state are obtained which, however, are too involved to be generally discussed. The theory can be applied to argon using the Lennard-Jones potential for the interaction between argon atoms, and the results are shown in diagrams. The character of the singularity separating liquid and gas can be seen from these diagrams to lie at the lowest point of the isotherm in the unstable region. An estimate of the position of the critical point is made and found in fair agreement with the experiental data.